Is there a reason why Turkey took the Balkan territories of the Ottoman Empire, instead of Greece or another of the Balkan states?

One must understand that the breakup of the Ottoman Empire, shortly after the end of the First World War, led to a political reconfiguration of greater Anatolia.

Much of present-day Turkey exists within the millennia old land of Anatolia-(then renamed, "Asia Minor" during The Roman Empire 2000 years ago). The contemporary country of Turkey exists, primarily due to the efforts and workings of Kemal Ataturk.

However, shortly before the rise of Kemal Ataturk, Anatolian Turkey, was essentially divided into various European territorial zones of occupation......this included, a Greek occupational zone, which returned the region of Ionia and in particular the city of Smyrna/(Izmir) to Greece in the year, 1919. However, the Hellenic controlled zone of Ionia and Smyrna only lasted 3 years and by 1922, the Greek population of Smyrna were literally chased out by Kemal Ataturk and the rabidly nationalistic Turkish military. The region of Ionia and he city of Smyrna/(Izmir), in particular, had been "ethnically cleansed" of its centuries old Greek population and the limited sovereignty that the Greeks had over Ionia and Smyrna-(as guaranteed by The Treaty of Sevres)....was discontinued.

Beginning in 1922-23, the Republic of Turkey was born whereby much of Turkey's present-day borders have remained largely unchanged in 100 years. Though it should also be noted that around the same time when the Republic of Turkey was founded, there was a population exchange between Greece and Turkey whereby hundreds of thousands-(or perhaps even millions) of Turkish Muslims living in Greece-(primarily, Northern Greece), were relocated to and exchanged with millions of Anatolian Greeks-(residing primarily in the Black Sea region) who were subsequently, relocated to Northern Greece.

As for present-day Istanbul, it is a city of about 6 million people, the vast majority of its residents are Turkish Muslims. The Greek Christian population-(which is primarily associated with the Orthodox Christian Patriarchate), numbers in the thousands. Judging from its demographics, the Greek Christian presence in present-day Istanbul, is nearly infinitesimal in size. In other words, the heyday of Byzantine Constantinople, is a historical memory whereby the impressively designed Dome of the Saint Sophia Cathedral....remains surrounded and punctuated by four minarets....and has remained so, since 1453.

Let's look at the map in 1913:

(click for large)
Detail view 1913:

^{Omniatlas: Europe 1913: Aftermath of the Balkan Wars}

^{"Greece according to the Treaty of Sèvres", in Wikipedia: Partition of the Ottoman Empire}

These tiny remnants of Rumelia on both maps are not overly meaningfully described as "Empire's Balkan holdings".

The Empire's Balkan holdings, or Rumelia, looked as recently as 1861 more like:

Or even in 1912:

So, after the Great War, Turkey only emerged from the ruins of the Ottoman Empire and just held the line at its western border? Compared to its former "Balkan holdings", this is a really tiny strip of land in the historic Marmara region.

During the Turkish War of Independence and especially the Greco-Turkish War (1919–1922) the chaotically mixed settlement patterns of Greeks, Turks, and 'others' made it not overly convenient to base any considerations for future borders on 'historic precedent', 'rights' or even 'majority populations'.
Contemplating something like "Istanbul and the Balkans should have been given to Greece" – for whatever historical reasons, going back to late antiquity even – would mean that any armchair diplomat proposing such would ignore the past 800 years of historical development and the then present situation on the ground. That is of course great for nationalist expansion and a terrible idea for peace.

To rephrase the initial question:
Q Was there a reason why Turkey retained the rest of the Balkan territories of the Ottoman Empire, instead of adding East-Thrace and Istanbul to Greece or another of the Balkan states?

Yes. The Paris Peace Conference had terrible ideas for the future borders of a post-Ottoman/Turkish state. That caused a war in which the participants wanted to decide the argument with force. Turkey emerged from that war less defeated compared to other prying eyes and was able to largely retain the borders in its West as agreed upon in the concluding Treaty of Lausanne.

The Greek front collapsed with the Turkish counter-attack in August 1922, and the war effectively ended with the recapture of Smyrna by the Turkish forces and the Great fire of Smyrna.

As a result, the Greek government accepted the demands of the Turkish national movement and returned to its pre-war borders, thus leaving East Thrace and Western Anatolia to Turkey.

The Allies abandoned the Treaty of Sèvres to negotiate a new treaty at Lausanne with the Turkish National Movement. The Treaty of Lausanne recognized the independence of the Republic of Turkey and its sovereignty over Asia Minor, Istanbul, and Eastern Thrace. Greek and Turkish governments agreed to engage in a population exchange.
_{WP: Greco-Turkish War (1919–1922)}